This invention provide utility-scale direct load control problem where the controlled loads are discrete-time zero-deadbandresidential thermostats that allow utility-dispatched microadjustments to the consumer's setpoint. These new digital thermostats serve as the basis for highly accurate direct load control systems, as well as price-based indirect load control systems. An aggregate load model is described and its fundamental characteristics are derived from first-principles. The aggregate load model is used to design a stable closed-loop load controllers for a discrete-time utility-scale demand response dispatch system. The control system is stable, controllable and observable and can work equally well with direct load control as with price-based indirect load control.